In this article, we prove convergence of the weakly penalized adaptive discontinuous
Galerkin methods. Unlike other works, we derive the contraction property for various
discontinuous Galerkin methods only assuming the stabilizing parameters are large enough
to stabilize the method. A central idea in the analysis is to construct an auxiliary
solution from the discontinuous Galerkin solution by a simple post processing. Based on
the auxiliary solution, we define the adaptive algorithm which guides to the convergence
of adaptive discontinuous Galerkin methods.

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.